90--110 DB (very OT)

[Bill Ballard]

At 3:23 PM -0500 12/1/02, Sarah Fox wrote:
>When two tones of slightly differing frequency are summated, there is a
>*perceived* beat frequency equal to the difference of the two frequencies.
>Each beat represents a complete "drift cycle" in which the two tones cycle
>from adding constructively to adding destructively to adding constructively
>again.  However there really isn't any acoustic energy at the difference
>frequency.

Would that be because the beat frequency only exists as a amplitude 
fluctuation of the peaks of the "carrier frequency". This would get 
to your "perceived frequency" as having now energy of its own.

This perception does get tricky. When one acoustical space is flooded 
with say, two standing waves (for this discussion ignore all but the 
fundamentals) of 440 and 442Hz, the summation process occurs in the 
atmosphere with its alternating cancellation and reinforcement. The 
result of this is heard by the human ear as a single pitch with an 
amplitude pulsation of 2Hz of some single tone ("carrier frequency"). 
The human ear has no direct way of measuring that carrier frequency, 
but a frequency counter capable of directly measurements would be 
useless  because , in its precision, it would insist that there were, 
yes two frequencies present in that one space.

My musical ear has no difficulty distinguishing between the two 
pitches, assuming they are not played simultaneously (in which case 
they sound like one, with a beat rate), but are played in series with 
a close enough time interval to allow the memory on which my relative 
pitch depends. But played together, my musical ear could not be 
convinced that there way anything but one tone at play. Would this be 
due to the fact that the summation of the two original tones is 
instantaneous, and replaces these two with a third tone.

IWO, to my ears, would there be any difference between a single 
440.5Hz pitch with a 2Hz pulse in its amplitude, and the result of 
two tones, 440 and 441Hz in one physical space? I'd like to know how 
a frequency counter hears this. Would it be able to point to two 
discrete tones, or would it be paralyzed by its inability to resolve 
on more than one frequency at a time.

>Beat frequency detection is really a perceptual phenomenon that lets us
>determine the periodicity (i.e. the fundamental) of a sound without energy
>being present at the fundamental.  If we are presented with 400+500+600,
>provided the relative phasing of these components doesn't drift, we hear
>100.

Is that because where these three frequencies are present, they in 
fact are the 4th, 5th, and 6th partials of a 100Hz fundamental? Or 
given any equally spaced trio of frequencies, will we hear the beat 
frequency any way, whether or not the original frequencies are in our 
hearing range, and whether or not the beat frequency itself is in the 
pulse or tone range of our hearing?

So we are right back to Richard Moody's question.

I thinks it's time to hook up two tweeters each to its own frequency 
generator, with an oscilloscope in between. Pick two original 
frequencies well within the hearing range, say 10KHz and 10.44KHz. 
(Their spread represents a comfortably audible frequency.) See if we 
can hear a 440Hz tone. And if we can't hear it, can a microphone 
plugged into an oscilloscope find it?

Bill Ballard RPT
NH Chapter, P.T.G.

"Talking about music is like dancing about architecture"
     ...........Steve Martin
++++++++++++++++++++